Grid-based modeling of materials can provide both geometric information and generalizability. Hoffman et al. explore the possibility of performing dimensionality reduction using deep learning models to encode and decode 3D crystal structures [1]}. Ragoza et al. [2]} use grids with Gaussian-like density functions for voxels to learn continuous representations of 3D molecular conformations. Our formalism builds on this by allowing for grids with variable spatial resolutions. Each grid can represent a different volume of space depending on the size of the material. This enables the model to learn multi-resolution representations of molecules. This allows us to represent different classes of materials that may have different numbers of atoms required to scale. As we integrate the atomic probability densities over voxel regions, we are also able to encode global molecule level features such as the total number of atoms, and the number of atoms per element. Furthermore, the discretization step described by Ragoza et al. utilizes a solver that uses gradient descent for atomic structure detection. They generate multiple possible structures per grid. They subsequently use beam search to find the best possible 3D structure. Similarly, Kim et al. use a 3D-GAN to generate crystal structures called, Zeolites [3]}.
